A Price Tag on Alpha II

October 8, 2017

... Part II of III

In A Price Tag on Alpha - Part I of this series, we barely covered alpha generation. All we did was put on the table an expression for the future value of the most expected portfolio outcome, this taken from the US stock market secular trend over durations of 20 and 30 years. We did provide a formula with the alpha considered but have not shown its long-term impact. Time to remedy that.

From chart #1 in Part I, the picture changes considerably if we add some alpha (see chart #3 below). Since the question was: What would people pay for performance of over 25% on a yearly basis? This would set the alpha to be the equivalent of a 15% CAGR.

What we have is just a change of scale. Yet, from $6.7 million in chart #1, the total is now $86.7 million. More than 10 times the outcome of chart #1. Therefore, an easy conclusion would be that this alpha does have some value.

#3 25% CAGR – 20 Years – With Random Path

(click to enlarge)

Chart #3 shows the impact of having a 25% CAGR over a 20-year time span. But still, it could be considered small should we add 10 years to the task as we did in chart #2 (see Part I).

#4 25% CAGR – 30 Years – With Random Path

(click to enlarge)

The behavior of the erratic curve changed even if the same equation for the random percent variations was used for all 4 charts. The first 20 years of chart #3 appear almost flat on chart #4. The final outcome is more than 9 times the first 20 years combined.

Chart #4 also compares the 10% CAGR to the output with the added 15% alpha. The difference might not be that noticeable in the beginning, but as we go along, the spread widens considerably. The final outcome for the erratic curve of chart #4 is more than 47 times the 10% CAGR of chart #1. From a different angle, this 15% in added alpha generated over 800 times its initial stake compared to 17 times for the zero-alpha scenario.

Therefore, the question remains: how much is that alpha worth?

The 2/20 Hedge Fund Scenario

To emulate a 2/20 hedge fund fee structure, I will use the expression: F0∙[(1+ rm + α∙(1 – c ) – 0.02)t – 1] where c is the charge on the alpha.

The above expression gives the total amount of profits made over the trading interval t starting with initial trading funds F0. The alpha is the added return the trading strategy brings to the game, while c is the charge one could assign as a fee on this overperformance. For instance, c equals 20% in this 2/20 hedge fund scenario. One could change the values given to these charges or add other fees.

Needing only a rough estimate, I will continue to use a 10% CAGR (including reinvested dividends) as the long-term average market return (rm). This return should be considered as given away almost free since we could buy low-cost index funds and get it with little effort.

It remains the portfolio's most expected long-term market return. Once again, we will consider as investment intervals of 20 and 30 years. Nonetheless, going forward, the average market return might be less than the exhibited secular market average. But we could still make estimates as to the long-term costs and effects on portfolio returns.

One might want to pay only for the alpha generation capabilities of a trading strategy since we have: α = ry – rm, where ry is the 25% CAGR mentioned in Part I. What is brought to the game can be easily estimated having this long-term expected value for rm.

Of note, most hedge funds add a pair of parenthesis on the above expression, and it does make a difference: F0∙[(1+ (rm + α)∙(1 – 0.20 ) – 0.02)t – 1 ]. The fees are charged on the total assets under management. Should the hedge fund generate no alpha, as many do, it could be quite a burden on an investor's portfolio to carry those 2/20 charges: F0∙[(1+ (rm + 0)∙(1 – 0.20 ) – 0.02)t – 1 ].

The hedge fund will not change its fee structure in less productive times, and most certainly not during their more productive periods. There could be a real detrimental impact on a portfolio should the long-term alpha be negative. In fact, you would be paying someone to lose your money on your behalf. It is ironic, but what could you do when the job has been done. You can only react after the fact. You could not know this in advance. Otherwise, you definitely would have taken a different course of action.

Is presented only one of the possibilities of fee structure. There are many more, but the task at hand is not to compare hedge fund fee structures, but to try to give a value to the alpha generation itself. Having a rough estimate might be sufficient. At least, it could be a starting point.

You help someone make more money than they themselves could have made on their own, then it appears only logical you should be rewarded. It is based on the same principles as any other kind of work someone would do for you. There should be some kind of remuneration or compensation for the work done or expertise provided.

Note that over the long term most portfolio managers have a hard time even getting the market's secular average, meaning that the alpha could be low, non-existent, and even negative.

If you look at academic literature, especially, the efficient market hypothesis, you should notice that the portfolio tangential to the efficient frontier entails an alpha of zero as the most expected outcome for a long-term portfolio. You have a lot of money riding on this logistic (in excess of 10 trillion dollars). Jensen, in his paper, in the late 60's put the average portfolio manager's alpha at -1.7%. That could not be considered as some form of over-performance, not by any stretch of the imagination.

Nonetheless, positive alpha can be had.

Some Numbers

Charts #1 to #4 all start with a $1M dollar fund. You can add or remove zeros, and the charts will look exactly the same. Only the scale will change. Therefore, should you want to consider larger or smaller funds, simply add or remove zeros on the vertical axis. You could do all this in Excel with ease.

All you would do is change F0, the initial capital at work. It is totally under your control. And is independent of what the market does. However, the alpha is all you. It is what you, your strategy, and even luck can bring to the game. It is your knowledge and expertise translated into code that will generate this alpha.

On a $1M dollar fund, in its first year, a 25% return would add $150k above rm's $100k. However, this would implicitly impose some added risk which should tend to mitigate the value of this alpha. Also, charging 20% on the alpha would definitely reduce the outcome.

The charge would be $30k (20%∙$150k). The fund would get $220k for its first year, which is the equivalent of having had a 22% CAGR. After taking away the 2% management fee, the fund would be left with a 20% CAGR. Still twice what they might have expected. To give it some perspective, Mr. Buffett over the years did manage to maintain the equivalent of 10% alpha.

The original 15% alpha still amounted to something. The investor got 10% alpha out of it representing 1,000 basis points. Still impressive.

If the calculation was performed on the total assets under management, then the 20% fee would result in a charge of $50k to which would be added the 2% management fee. This would reduce the total outcome for the investor to an 18% CAGR. This remains above the most expected long-term market outcome of a 10% CAGR. So, there is still value there.

Should you take off a zero on this fund, the picture changes drastically. Now, the charges go down to $3k for the alpha and $2k on fees. I can not say it would be a great motivator for doing any work, day in and day out, on this $100k fund. There definitely appears to be a lower limit to the initial fund which renders it utterly unproductive spending any time on, even if you could provide a 25% CAGR.

A relevant question could be: how much more risk does someone have to take to get this extra 15% CAGR? If it is only someone's word that ascertains this risk, I would instantly say: count me out. There is a need for a suitable demonstration to show that it could be there, even if the future remains unknown.